Problem: Wyatt is making a salad using tomatoes, cucumbers, and carrots. This table gives the cost, per kilogram, of each ingredient, and the amount, in kilograms, that Wyatt uses: Ingredient Price per kilogram Amount Tomatoes $3.30$ dollars per kilogram $0.3$ kilograms Cucumbers $x$ dollars per kilogram $y$ kilograms Carrots $z$ dollars per kilogram $0.2$ kilograms The total amount Wyatt spends on ingredients is $C$ dollars. Write an equation that relates $x$, $y$, $z$, and $C$.
Let's find the amount of money Wyatt spends on each ingredient. Then we can add all these up to find the total sum. For example, tomatoes costs $3.30$ dollars per kilogram and Wyatt uses $0.3$ kilograms of them, so Wyatt spends $3.30\cdot 0.3=0.99$ dollars on tomatoes: $\begin{aligned} &\phantom{=}\left(3.30\,\dfrac{\text{dollars}}{\text{kilogram}}\right)\left(0.3\,\text{kilograms}\right) \\\\ &=3.30\cdot 0.3\,\dfrac{\text{dollars}}{\cancel\text{kilogram}}\cdot\,\cancel\text{kilograms} \\\\ &=0.99\,\text{dollars} \end{aligned}$ Similarly, Wyatt spends $x\cdot y$ dollars on cucumbers and $0.2z$ dollars on carrots. Ingredient Price per kilogram Amount ${\text{Price}}$ Tomatoes $3.30$ dollars per kilogram $0.3$ kilograms ${0.99\text{ dollars}}$ Cucumbers $x$ dollars per kilogram $y$ kilograms ${xy\text{ dollars}}$ Carrots $z$ dollars per kilogram $0.2$ kilograms ${0.2z\text{ dollars}}$ The total amount Wyatt spends on ingredients is the sum of the prices of each ingredient: $C=0.99+xy+0.2z$